To improve the bulging property at normal temperature, and to improve the machining limit by achieving the heat treatment at a heating temperature before the grain growth in the steel of a stainless steel cylindrical member having the working distortion of not less than the specified quantity, removing the working distortion, and then, achieving the bulging.

Since the stainless steel cylindrical member having the working distortion of not less than 8% has much accumulated distortion energy, the grain grows and the bulging property is degraded in the heat treatment same as that for a stainless steel cylindrical member having the working distortion of less than 8%. Thus, the working distortion is eliminated at the heat treatment temperature before the grain growth to achieve the bulging. The heat treatment temperature is 700-900°C, and the heat treatment is achieved at a temperature lower than the heat treatment temperature for the stainless steel cylindrical member having the working distortion less than 8%. The working distortion is surely eliminated thereby while preventing the grain growth in the steel, and the bulging property in the bulging process is improved.